Related papers: An It\^o-type formula for some measure-valued proc…
Earlier we presented a method to decompose modal formulas for processes with the internal action $\tau$, and congruence formats for branching and $\eta$-bisimilarity were derived on the basis of this decomposition method. The idea is that a…
The paper studies a system of first order Hamilton-Jacobi equations with discontinuous coefficients, arising from a model of deterministic optimal debt management in infinite time horizon, with exponential discount and currency devaluation.…
We consider the problem of rare event importance sampling, where the random variable of interest is a path functional of an It\^o diffusion computed up to the first exit from a $d$-dimensional bounded domain. Dupuis and Wang (\textit{Ann.…
Sharp temporal decay estimates are established for the gradient and time derivative of solutions to a viscous Hamilton-Jacobi equation as well the associated Hamilton-Jacobi equation. Special care is given to the dependence of the estimates…
We introduce a new numerical method to approximate the solution of a finite horizon deterministic optimal control problem. We exploit two Hamilton-Jacobi-Bellman PDE, arising by considering the dynamics in forward and backward time. This…
In this paper, we explore a new class of stochastic control problems characterized by specific control constraints. Specifically, the admissible controls are subject to the ratcheting constraint, meaning they must be non-decreasing over…
We prove the uniqueness of the viscosity solution to the Hamilton-Jacobi equation associated with a Bolza problem of the Calculus of Variations, assuming that the Lagrangian is autonomous, continuous, superlinear, and satisfies the usual…
We propose a globally convergent numerical method, called the convexification, to numerically compute the viscosity solution to first-order Hamilton-Jacobi equations through the vanishing viscosity process where the viscosity parameter is a…
We study a stochastic optimal control problem for a partially observed diffusion. By using the control randomization method in [4], we prove a corresponding randomized dynamic programming principle (DPP) for the value function, which is…
A well-known It\^o formula for finite dimensional processes, given in terms of stochastic integrals with respect to Wiener processes and Poisson random measures, is revisited and is revised. The revised formula, which corresponds to the…
We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated…
We introduce a stochastic version of the optimal transport problem. We provide an analysis by means of the study of the associated Hamilton-Jacobi-Bellman equation, which is set on the set of probability measures. We introduce a new…
We study the stochastic control-stopping problem when the data are of polynomial growth. The approach is based on backward stochastic dierential equations (BSDEs for short). The problem turns into the study of a specic reected BSDE with a…
We use a rough path-based approach to investigate the degeneracy problem in the context of pathwise control. We extend the framework developed in arXiv:1902.05434 to treat admissible controls from a suitable class of H\"older continuous…
In this paper, we focus on the stochastic representation of a system of coupled Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs (HJBI), for short) equations which is in fact a system of coupled Isaacs' type integral-partial differential…
Recently, functional It\=o calculus has been introduced and developed in finite dimension for functionals of continuous semimartingales. With different techniques, we develop a functional It\=o calculus for functionals of Hilbert…
The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the…
In the paper, we consider a path-dependent Hamilton-Jacobi equation with coinvariant derivatives over the space of continuous functions. Such equations arise from optimal control problems and differential games for time-delay systems. We…
In this note we study the convergence of monotone P1 finite element methods on unstructured meshes for fully non-linear Hamilton-Jacobi-Bellman equations arising from stochastic optimal control problems with possibly degenerate, isotropic…
We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…